Channel-Optimized Strategic Quantization

This paper studies a quantization problem between an encoder and a decoder with misaligned objectives, where the quantization indices are transmitted over a noisy channel. Building on the prior results on the non-strategic counterpart of this problem, we characterize the encoding and decoding strategies and expected encoder and decoder distortions at the Stackelberg equilibrium, where the encoder is the leader, and the decoder is the follower. On the design side, we extend the gradient-descent-based solution framework developed for the noiseless setting to this noisy communication scenario, combined with uniformly randomized index mapping. We finally present numerical simulation results to demonstrate the efficacy of the proposed approach. The Matlab codes associated with the design and evaluation of the proposed algorithm are provided at: https://github.com/strategic-quantization/channel-optimized-strategic-quantizer.